Final answer:
The quantities that have the dimensions of speed are √(2x/a) and √(2ax).
Step-by-step explanation:
The quantities that have the dimensions of speed are b. √(2x/a) and c. √(2ax).
In option b, √(2x/a), x represents displacement and a represents acceleration. When a displacement is divided by an acceleration, the result is in the units of time (T). Therefore, √(2x/a) has the dimensions of speed, which are distance per time (L/T).
In option c, √(2ax), a represents acceleration and x represents displacement. When an acceleration is multiplied by a displacement, the result is in the units of velocity (LT⁻¹). Therefore, √(2ax) has the dimensions of speed, which are velocity (LT⁻¹).